An equation with the same solution as another is an equivalent equation: the same value must make both true. One route is to find the variable’s value with a Desmos regression, then evaluate the expression shared by the choices. Watch the subtraction: removing a term from only one side changes the solution.
Hints
- Hint 1
A solution is a value of that makes both sides of the given equation equal. To find it with a Desmos regression, replace with and replace with .
- Hint 2
Every option has the same left side, . Once you know the original solution, put that value into . Which right side matches the value you get?
Step-by-step
Find the solution, then evaluate
Step 1Find the original solution
A solution makes the two sides equal. Type in Desmos. Here stands for the problem’s , and tells Desmos to find its value. Under PARAMETERS, Desmos shows , so the original solution is .
- Step 2
Find the right side that matches
All the choices start with , so evaluate that shared expression at the solution. Type on the next Desmos line. It uses and prints . So has the original solution. The in the given equation is what remains after subtracting from ; it isn’t the value of . Choice C.